After a theoretical model showed that observed intraspecific variability can emerge from environmental heterogeneity and an experimental clonal dataset showed that a significant part of intraspecific variability in growth is not due to the genotype, we here want to examine the features of three natural tropical forest. One is located in French Guiana (Paracou), another is located in the Whestern Ghats in India (Uppangala) and the last one is located in Panama (Barro Colorado island, denoted BCI). The analyses will follow the ones done on the virtual dataset generated with the theoretical model. Indeed, this will help making connexions between theory and observations. First, we will estimate the intraspecific variance of annualised growth in the three datasets using a hierachical bayesian model. Then, we will test if we can detect spatial structure in individual mean growth. Finally, we will test if intraspecific variability is higher than interspecific variability.
The Paracou forest is located in French Guiana. It is one of the best-studied lowland tropical forests in the Guiana Shield region. It belongs to the Caesalpiniaceae facies and has amongst the highest alpha-diversity in the Guiana shield with 150-200 tree species per hectare in inventories of trees with diameter at breast height (DBH) \(\ge\) 10 cm [1]. The studied area gathers 768 species on 93,75 ha corresponding to 254 genus of 65 plant families. The Guiana Shield is characterized by Pre-Cambrian granitic and metamorphic geological formations, highly eroded. It is associated with gently undulating landscapes and a very dense hydrographic system. Paracou forest lies in a hilly area, on a formation called “série Armina” characterized by schists and sandstones and locally crossed by veins of pegmatite, aplite and quartz. The topography of the site consists of small hills separated by narrow ( < 5 m wide) sandy waterbeds. The altitude varies from 5 to about 45 m above sea level [1]. The mean annual temperature is of 26 °C and winds are generally weak. There is a well marked dry season (from mid-August to mid-November) and a long rain season with a short drier period between March and April (mean annual rainfall of 3,041 mm). Different study programs have been led at the Paracou site, which is managed by the CIRAD but is open to the scientific community. Here, we have used a silvicultural experiment called the “disturbance experiment” under which 15 plots of 6,25 ha were exposed to four different logging conditions between 1986 and 1988. Since then, cartesian coordinates, DBH, species identity and survival for each tree with a DBH \(\ge\) 10 cm has been collected every one or two years, during the dry season (mid-August to mid-November). This represents about 46000 trees in total.
Uppangala Permanent Sample Plot (UPSP) is located in South-East Asia, in the Western Ghats of India, established in 1089 by the French Institute of Pondicherry in the Kadamakal Reserve Forest, in the Pushpagiri Wildlife Sanctuary, in Karnataka state, India [3]. It is a low altitude (500-600 m) wet evergreen monsoon Dipterocarp forest [4]. The studied area, of 5.07 ha, is quite steep, with a mean slope angle of about 30–35°. The plots are five north–south oriented transects, 20 m wide, 180 to 370 m long, and 100 m apart center to center and three rectangular plots which overlap the transects. The transects gather data from 1990 to 2011 and the rectangular plots from 1993 to 2011. The trees with GBH (Girth at Breast Height) \(\ge\) 30 cm (equivalent to about 9.5 cm DBH) were measured every 3 to 5 years. The raw dataset contains 3870 trees and 102 species (including 2 morphospecies). This forest is considered as one of the rare undisturbed tropical forests in the world [5].
The Barro Colorado Island site is located in central America, in Panama, covered by a lowland tropical moist forest. The zone became an island after a valley was flooded in order to build the Panama Canal, in 1913. It is nowadays considered as the most intensively studied tropical forest in the world. The studied site is a 50 ha plot (500 \(\times\) 1000 m). It has an elevation of 120 m and is quite flat (most slopes are gentler than 10°). Complete censuses of all trees with DBH \(\ge\) 1 cm were performed every 5 years since 1980. In the raw data, there are 328 tree species and 423617 trees and when only taking into account trees with DBH \(\ge\) 10 cm, there are 255 species and 37224 trees. The data is available in [6].
Here is the head of the dataset :
| Forest | Plot | PlotArea | SubPlot | TreeFieldNum | idTree | Xfield |
|---|---|---|---|---|---|---|
| Paracou | 1 | 6.25 | 1 | 1 | 75475 | 5 |
| Paracou | 1 | 6.25 | 1 | 1 | 75475 | 5 |
| Paracou | 1 | 6.25 | 1 | 1 | 75475 | 5 |
| Paracou | 1 | 6.25 | 1 | 1 | 75475 | 5 |
| Paracou | 1 | 6.25 | 1 | 1 | 75475 | 5 |
| Paracou | 1 | 6.25 | 1 | 1 | 75475 | 5 |
| Yfield | Xutm | Yutm | Lat | Lon | Family | Genus |
|---|---|---|---|---|---|---|
| 125.5 | 285109.6 | 582983.2 | 5.271257 | -52.93895 | Euphorbiaceae | Conceveiba |
| 125.5 | 285109.6 | 582983.2 | 5.271257 | -52.93895 | Euphorbiaceae | Conceveiba |
| 125.5 | 285109.6 | 582983.2 | 5.271257 | -52.93895 | Euphorbiaceae | Conceveiba |
| 125.5 | 285109.6 | 582983.2 | 5.271257 | -52.93895 | Euphorbiaceae | Conceveiba |
| 125.5 | 285109.6 | 582983.2 | 5.271257 | -52.93895 | Euphorbiaceae | Conceveiba |
| 125.5 | 285109.6 | 582983.2 | 5.271257 | -52.93895 | Euphorbiaceae | Conceveiba |
| Species | BotaSource | BotaCertainty | idVern | VernName | CommercialSp | CensusYear |
|---|---|---|---|---|---|---|
| guianensis | Bota | 4 | 601 | kusisi | 0 | 1984 |
| guianensis | Bota | 4 | 601 | kusisi | 0 | 1985 |
| guianensis | Bota | 4 | 601 | kusisi | 0 | 1986 |
| guianensis | Bota | 4 | 601 | kusisi | 0 | 1987 |
| guianensis | Bota | 4 | 601 | kusisi | 0 | 1988 |
| guianensis | Bota | 4 | 601 | kusisi | 0 | 1989 |
| CensusDate | CensusDateCertainty | CodeAlive | MeasCode | Circ | CircCorr | CorrCode |
|---|---|---|---|---|---|---|
| 1984-09-01 | 1 | 1 | 0 | 50.5 | 50.5 | 0 |
| 1985-11-01 | 1 | 1 | 0 | 51.5 | 51.5 | 0 |
| 1986-10-01 | 1 | 1 | 0 | 51.0 | 51.0 | 0 |
| 1987-10-01 | 1 | 1 | 0 | 51.0 | 51.0 | 0 |
| 1988-09-01 | 1 | 1 | 0 | 51.0 | 51.0 | 0 |
| 1989-10-01 | 1 | 1 | 0 | 51.0 | 51.0 | 0 |
Here is a plot of the trees :
Figure 2.1: Plots at the Paracou site. Each point is a tree.
There are 760 species, 90262 trees and 1448802 observations in this dataset.
Here are the new columns created :
| D_tp1 | D_tp1_corr | D_t | D_t_corr | Date_tp1 | Date_t | DiffD | DiffD_corr |
|---|---|---|---|---|---|---|---|
| 16.39296 | 16.39296 | 16.07465 | 16.07465 | 1985-11-01 | 1984-09-01 | 0.3183099 | 0.3183099 |
| 16.23380 | 16.23380 | 16.39296 | 16.39296 | 1986-10-01 | 1985-11-01 | -0.1591549 | -0.1591549 |
| 16.23380 | 16.23380 | 16.23380 | 16.23380 | 1987-10-01 | 1986-10-01 | 0.0000000 | 0.0000000 |
| 16.23380 | 16.23380 | 16.23380 | 16.23380 | 1988-09-01 | 1987-10-01 | 0.0000000 | 0.0000000 |
| 16.23380 | 16.23380 | 16.23380 | 16.23380 | 1989-10-01 | 1988-09-01 | 0.0000000 | 0.0000000 |
| 16.23380 | 16.23380 | 16.23380 | 16.23380 | 1990-10-01 | 1989-10-01 | 0.0000000 | 0.0000000 |
| DiffDate | G_tp1 | G_tp1_corr | Tree | Sp | IdentSpecies |
|---|---|---|---|---|---|
| 426 days | 2.727303 | 2.727303 | P1T75475 | Conceveiba_guianensis | 86 |
| 334 days | -1.739268 | -1.739268 | P1T75475 | Conceveiba_guianensis | 86 |
| 365 days | 0.000000 | 0.000000 | P1T75475 | Conceveiba_guianensis | 86 |
| 336 days | 0.000000 | 0.000000 | P1T75475 | Conceveiba_guianensis | 86 |
| 395 days | 0.000000 | 0.000000 | P1T75475 | Conceveiba_guianensis | 86 |
| 365 days | 0.000000 | 0.000000 | P1T75475 | Conceveiba_guianensis | 86 |
There are 615 species and 78434 and 1053241 trees at this step.
Individual mean growth is computed as the diameter difference between the first and the last census divided by the number of years between these two censuses. It is thus annualised.
| Tree | Sp | IdentSpecies | Mean_G_Tree |
|---|---|---|---|
| P10T120923 | Protium_surinamense | 461 | 1.150808 |
| P10T120924 | Licania_alba | 297 | 1.029670 |
| P10T120925 | Indet_sp | 225 | 4.300386 |
| P10T120926 | Indet_sp | 225 | 2.665028 |
| P10T120927 | Licania_alba | 297 | 1.029670 |
| P10T120928 | Indet_sp | 225 | 4.542661 |
| TreeID | CensusDate | Girth | Recruited | GirthError | GirthNote | SpCode | Xsite | |
|---|---|---|---|---|---|---|---|---|
| 2 | A001 | 1994-11 | 73.78 | NA | NA | NA | vain | 650.05 |
| 4 | A001 | 1990-11 | 71.98 | NA | G3 | new belt fixed | vain | 650.05 |
| 5 | A001 | 1991-11 | 73.16 | NA | NA | NA | vain | 650.05 |
| 8 | A001 | 2000-12 | 73.76 | NA | NA | NA | vain | 650.05 |
| 9 | A001 | 2001-12 | 74.02 | NA | NA | NA | vain | 650.05 |
| 10 | A001 | 1993-11 | 73.62 | NA | NA | NA | vain | 650.05 |
| Ysite | slope | aspect | PotStrata | death.cause | date | Plot | SubPlot | |
|---|---|---|---|---|---|---|---|---|
| 2 | 56.35 | 36.13096 | 67.08345 | 0 | NA | 1704 | A | Aa01 |
| 4 | 56.35 | 36.13096 | 67.08345 | 0 | NA | 244 | A | Aa01 |
| 5 | 56.35 | 36.13096 | 67.08345 | 0 | NA | 609 | A | Aa01 |
| 8 | 56.35 | 36.13096 | 67.08345 | 0 | NA | 3926 | A | Aa01 |
| 9 | 56.35 | 36.13096 | 67.08345 | 0 | NA | 4292 | A | Aa01 |
| 10 | 56.35 | 36.13096 | 67.08345 | 0 | NA | 1339 | A | Aa01 |
Here is the plot of the trees :
Figure 2.2: Plots at Uppangala site. Each point is a tree.
There are 102 species, 3870 and 69459 observations in this dataset.
We remove the census dates which were not common for all plots.
Compute annual growth
Remove lines with a growth higher than 100 mm/y or inferior to -2 mm/y.
Thus there are 102 species, 3725 trees and 57921 observations after annual growth computation.
Here are the computed columns :
| Date_tp1 | D_t | Date_t | DiffD | DiffDate | G_tp1 | Mean_G_Tree | Tree |
|---|---|---|---|---|---|---|---|
| 1995-11-01 | 23.48490 | 1994-11-01 | 0.0127324 | 365 days | 0.1273240 | 0.3466920 | A001 |
| 1995-11-01 | 65.72463 | 1994-11-01 | -0.0063662 | 365 days | -0.0636620 | -0.3339966 | A002 |
| 1995-11-01 | 31.72913 | 1994-11-01 | 0.5602254 | 365 days | 5.6022540 | 2.3360440 | A003 |
| 1995-11-01 | 28.11313 | 1994-11-01 | 0.5220282 | 365 days | 5.2202821 | 2.2204800 | A004 |
| 1995-11-01 | 14.51493 | 1994-11-01 | 0.0763944 | 365 days | 0.7639437 | 0.5945981 | A005 |
| 1995-11-01 | 10.52969 | 1994-11-01 | 0.0572958 | 365 days | 0.5729578 | 0.4127286 | A006 |
There are 328 species, 423617 trees and 3388936 observations in this dataset.
Here is the plot of the trees :
Figure 2.3: The 50 ha plot of the Barro Colorado Island site. Each point is a tree.
Compute annual growth
Remove lines with a growth higher than 100 mm/y or inferior to -2 mm/y.
There are now 244 species and 30386 trees and 167618 observations.
Finally, homogenise the three datasets.
These diagrams can help to visualise how diverse the tropical forest is, but also that there are few dominant species and many rare species (long threshold).
Figure 3.1: Abundance diagrams of each site
We need to estimate the importance of intraspecific variability compared to interspecific variability. To do so, we chose Stan to run a Bayesian hierarchical model, with a species random effect and an individual random effect on the intercept. In order to approach more classic growth models, we also added an intercept and a diameter fixed effect. We use the brms package to implement the model. We scale the data to improve convergence time.
\(ln(G_{ijt} + 2) = [\beta_0 + b_{0j} + d_{0i}] + \beta_1 \times ln(D_{ijt}) + \epsilon_{ijt},\)
Priors
\(\beta_0 \sim \mathcal{N}(mean=0, var = 1), iid\)
\(\beta_1 \sim \mathcal{N}(mean=0, var = 1), iid\)
\(b_{0j} \sim \mathcal{N}(mean=0, var=V_b), iid\)
\(d_{0j} \sim \mathcal{N}(mean=0, var=V_d), iid\)
\(\epsilon_{ijt} \sim \mathcal{N}(mean=0, var=V), iid\)
Hyperpriors
\(V_b \sim \mathcal{IG}(shape = 10^{-3}, rate = 10^{-3}), iid\)
\(V_d \sim \mathcal{IG}(shape = 10^{-3}, rate = 10^{-3}), iid\)
\(V \sim \mathcal{IG}(shape = 10^{-3}, rate = 10^{-3}), iid\)
Where \(i\) is the individual and \(j\) the species. The model includes two fixed effects (\(\beta_0\) and \(\beta_1\)), a random species effect \(b_{0j}\) on the intercept and a random individual effect \(d_{0i}\) on the intercept. \(V_d\) is the intraspecific variance and \(V_b\) is the interspecific variance.
## No divergences to plot.
Figure 4.1: Trace of the posterior estimates for Paracou
Figure 4.2: Density of the posterior estimates for Paracou
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: logG ~ 1 + logD + (1 | IdentSpecies) + (1 | IdentTree)
## Data: Data_stan_Paracou (Number of observations: 100000)
## Samples: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 2000
##
## Group-Level Effects:
## ~IdentSpecies (Number of levels: 575)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.47 0.02 0.44 0.50 1.01 255 471
##
## ~IdentTree (Number of levels: 48636)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.46 0.00 0.45 0.47 1.00 484 928
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.06 0.02 0.01 0.11 1.02 116 199
## logD 0.03 0.00 0.03 0.04 1.00 2094 1634
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.77 0.00 0.76 0.77 1.00 961 1340
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Here the intraspecific variability is about the same as interspecific variability.
We apply the same model on the Uppangala dataset.
## No divergences to plot.
Figure 4.3: Trace of the posterior estimates for Paracou
Figure 4.4: Density of the posterior estimates for Uppangala
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: logG ~ 1 + logD + (1 | IdentSpecies) + (1 | IdentTree)
## Data: Data_stan_Uppangala (Number of observations: 52524)
## Samples: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 2000
##
## Group-Level Effects:
## ~IdentSpecies (Number of levels: 99)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.38 0.04 0.30 0.47 1.00 294 487
##
## ~IdentTree (Number of levels: 3645)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.66 0.01 0.64 0.67 1.01 233 744
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.09 0.05 0.01 0.19 1.00 474 825
## logD 0.19 0.01 0.16 0.21 1.01 341 687
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.59 0.00 0.59 0.60 1.00 2620 1069
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
We can also conclude that intraspecific variability is high, but even that it is higher than interspecific variability.
We apply the same model to the BCI dataset.
## No divergences to plot.
Figure 4.5: Trace of the posterior estimates for BCI
Figure 4.6: Density of the posterior estimates for BCI
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: logG ~ 1 + logD + (1 | IdentSpecies) + (1 | IdentTree)
## Data: Data_stan_BCI (Number of observations: 110710)
## Samples: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 2000
##
## Group-Level Effects:
## ~IdentSpecies (Number of levels: 231)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.67 0.04 0.60 0.75 1.01 62 208
##
## ~IdentTree (Number of levels: 24320)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.41 0.00 0.40 0.42 1.00 565 1031
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.18 0.04 0.10 0.27 1.03 44 80
## logD -0.02 0.00 -0.03 -0.01 1.00 653 1276
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.81 0.00 0.81 0.82 1.00 1446 1686
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Here, intraspecific variability is slower than interspecific variability, although it is still about half the order of magnitude, which is significant. Note that here the mean estimated fixed effect of diameter on growth is slightly negative, which is counter-intuitive.
The following table enables to compare the results of the models for the three datasets.
| Intercept (\(\beta_0\)) | Diameter (\(\beta_1\)) | Species variance (\(V_b\)) | Individual variance (\(V_d\)) | Residual variance (\(V\)) | |
|---|---|---|---|---|---|
| Paracou | |||||
| Estimate | 6.4e-02 | 3.3e-02 | 4.7e-01 | 4.6e-01 | 7.7e-01 |
| Estimation error | 2.4e-02 | 4e-03 | 1.7e-02 | 4.1e-03 | 2.3e-03 |
| Uppangala | |||||
| Estimate | 9.5e-02 | 1.9e-01 | 3.8e-01 | 6.6e-01 | 5.9e-01 |
| Estimation error | 4.7e-02 | 1.2e-02 | 4.4e-02 | 8.6e-03 | 1.9e-03 |
| BCI | |||||
| Estimate | 1.8e-01 | -2.2e-02 | 6.7e-01 | 4.1e-01 | 8.1e-01 |
| Estimation error | 4.3e-02 | 4.6e-03 | 3.7e-02 | 4.1e-03 | 2e-03 |
We compute the proportion of unexplained variance of growth that is contained in the individual effects :
Figure 4.7: Proportions of each variance components for the three datasets. The variance of individual effects is in blue, the variance of species effect is in purple and the variance of residuals is yellow
Overall, a large part of variability is imputable to individual effects, showing a high intraspecific variability in growth in tropical forests, independently from the diameter effect.
In order to have a numeric evaluation of spatial autocorrelation, we perform Moran’s test on individual mean growth for each species. Moran’s test function function was re-written from the ape package’s Moran.I function in order to be able to select the pairs of neighbours which are less than 100 m apart. The p-values are obtained with a “greater” alternative hypothesis.
As this analysis takes time, we only present the graphical result from a previously obtained result, but feel free to re-run it from the .Rmd file.
We compute the proportion of species with significant positive spatial autocorrelation with a 0.05 alpha risk and the proportion of species with non significant spatial autocorrelation. The proportions are computed relative to the species on which the test was computed.
| Significant (i) | Not significant (ii) | |
|---|---|---|
| Paracou | ||
| Proportion of species | 28.7 | 71.3 |
| Proportion of individuals | 77.7 | 22.3 |
| Uppangala | ||
| Proportion of species | 18.5 | 81.5 |
| Proportion of individuals | 45.3 | 54.7 |
| BCI | ||
| Proportion of species | 16.9 | 83.1 |
| Proportion of individuals | 51.4 | 48.6 |
We can observe that the proportion of species with significant spatial autocorrelation is low (29% in Paracou, 18% for Uppangala, 17% for BCI). However, the mean number of individuals per category shows that there is a much higher number of individuals in species with significant spatial autocorrelation. This motivates to analyse the proportion of individuals represented in each category.
We test if species abundance significantly explains the significance of Moran’s test :
##
## Call:
## glm(formula = factor(signif) ~ nb_ind, family = binomial(link = "logit"),
## data = na.omit(Moran_I_Paracou))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -5.0432 -0.5836 -0.5083 0.0470 2.0907
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.140573 0.196665 -10.884 < 2e-16 ***
## nb_ind 0.010620 0.001518 6.995 2.65e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 455.47 on 379 degrees of freedom
## Residual deviance: 317.97 on 378 degrees of freedom
## AIC: 321.97
##
## Number of Fisher Scoring iterations: 7
##
## Call:
## glm(formula = factor(signif) ~ nb_ind, family = binomial(link = "logit"),
## data = na.omit(Moran_I_Uppangala))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9313 -0.5575 -0.5338 -0.5228 2.0219
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.957224 0.439264 -4.456 8.36e-06 ***
## nb_ind 0.005754 0.002750 2.093 0.0364 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 51.75 on 53 degrees of freedom
## Residual deviance: 46.27 on 52 degrees of freedom
## AIC: 50.27
##
## Number of Fisher Scoring iterations: 4
##
## Call:
## glm(formula = factor(signif) ~ nb_ind, family = binomial(link = "logit"),
## data = na.omit(Moran_I_BCI))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0333 -0.4755 -0.4223 -0.4016 2.2617
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.527817 0.317787 -7.954 1.80e-15 ***
## nb_ind 0.005645 0.001334 4.233 2.31e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 156.06 on 171 degrees of freedom
## Residual deviance: 122.57 on 170 degrees of freedom
## AIC: 126.57
##
## Number of Fisher Scoring iterations: 5
For all three datasets, the effect of the number of individuals on test significance is significant. However, it is less significant in Uppangala.
For Paracou, the proportion of individuals belonging to as species which had a significant spatial autocorrelation is high (> 77%). For Uppangala and BCI, it is lower (~45% and 51% respectively).
Important parameters contrasting between those forests are the topography, which is hillier in Uppangala, the number of species and of individuals per species, which are higher in Paracou, and the date of the last known disturbance, which is much more recent in Paracou than in BCI and Uppangala. Moreover, the same analysis of the undisturbed plots of Paracou give about the same proportion of individuals (exposed lower).
Finally, the magnitude of spatial autocorrelation varied across the three sites, with Paracou presenting the biggest proportion and Uppangala the lowest, which can be related to each site specificities. The plots of the Paracou site were subjected to disturbance treatments that created numerous large gaps [7]. This resulted in a high heterogeneity and spatial structuration of the environment. When restricting our analysis to undisturbed control plots, the proportion of detected spatial autocorrelation in conspecific growth drops from 77.1% to about 50% individuals, supporting the hypothesis that the more important spatial autocorrelation in Paracou is due to the stronger spatial structuration of the micro-environment associated with disturbance treatments. Conversely, the disturbance regime in BCI is known to produce frequent small gaps [8], while the mature forest in Uppangala has been reported as barely disturbed [3]. We acknowledge that the hilly topography of Uppangala could make our estimates of distances among individuals based on pairs of tree coordinates provided by field inventory less accurate than in the other two flatter sites.
In order to compare intra vs interspecific variance, we compute the semivariance of growth of individuals that are less than 100 m apart. We compare the semivariances obtained with conspecifics and heterospecifics with a Mann-Whitney test. Intraspecific variance is estimated with the semivariance computed as the squared difference of the mean growth of all pairs individuals of the focal species which are less than 100 m apart. Interspecific variance is estimated with the semivariance computed as the squared difference of the mean growth of all pairs individuals of the containing the focal species and another species which are less than 100 m apart.
Here again, the analysis is long to run and we display results from a pre-generated result.
| Intraspecific variability < interspecific variability (i) | Intraspecific variability ~ interspecific variability (ii) | Intraspecific variability > interspecific variability (iii) | |
|---|---|---|---|
| Paracou | |||
| Proportion of species | 63.3 | 36.3 | 0.333 |
| Proportion of individuals | 89.4 | 10.5 | 0.0699 |
| Uppangala | |||
| Proportion of species | 44.4 | 53.3 | 2.22 |
| Proportion of individuals | 59.2 | 22.4 | 18.4 |
| BCI | |||
| Proportion of species | 48.4 | 48.4 | 3.14 |
| Proportion of individuals | 75.7 | 19.6 | 4.69 |
We can see that in all forests, in about half of the species, local intraspecific growth semivariance is significantly smaller than local semivariance of heterospecifics growth.
In all forests, a large majority of individuals belong to species in which intraspecific growth semivariance is significantly smaller than interspecifc growth semivariance.
One of our main hypotheses is that many environmental variables are spatially structured. Consequently, as growth is largely influenced by environmental variables like light, it should also be spatially structured. Our analysis using Moran’s I test showed that growth was indeed spatially structured. The Paracou dataset offers the opportunity to test this hypothesis further. Indeed, some plots were disturbed in the early eighties, creating artificial gaps, whereas others were not disturbed. As the creation of gaps results in a strong spatial structure of the available light under the canopy, growth should be less structured in plots that were not disturbed. That is what we test here.
This leads to a dataset containing 14266 trees of 451 species.
| Significant (i) | Not significant (ii) | |
|---|---|---|
| Proportion of species | 18 | 82 |
| Proportion of individuals | 54.7 | 45.3 |
The proportion of individuals represented in the species which have a significant Moran’s test are about 50%. With the disturbed plots, it was more than 70%. This is due to the openness of the canopy triggering important spatial structure in disturbed plots due to light gap. In these gaps, tree tend to grow faster, and therefore the spatial structure of growth is stronger.
In order to be able to compare all three datasets together, we removed all stems that had a DBH inferior to 10 cm in BCI, where all stems with DBH \(\ge\) 1 cm are measured. Using the complete dataset, we concluded that the spatial structure in individual growth was even more significant.
We here used data on tree growth, which is one component of individual fitness and an imperfect proxy of tree competitive ability, and our analyses could be further tested with other traits in the future.
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